Problem: Solve for $x$ and $y$ using elimination. ${-6x+2y = -44}$ ${3x+5y = 52}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${-6x+2y = -44}$ $6x+10y = 104$ Add the top and bottom equations together. $12y = 60$ $\dfrac{12y}{{12}} = \dfrac{60}{{12}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-6x+2y = -44}\thinspace$ to find $x$ ${-6x + 2}{(5)}{= -44}$ $-6x+10 = -44$ $-6x+10{-10} = -44{-10}$ $-6x = -54$ $\dfrac{-6x}{{-6}} = \dfrac{-54}{{-6}}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {3x+5y = 52}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(5)}{= 52}$ ${x = 9}$